12  Assignment 5

Functions, loops, atomic vectors and matrices

12.1 Phrase search

Write a function that accepts a sentence and a phrase as parameters, and returns the number of times the phrase occurs in the string.

Call the function with the following sentence and phrase:

Sentence: “She sells the sea shells on the sea shore during the summer. She sits on the rocks, and reads the book on the horizon”,

Phrase: “on the”

12.2 Prime Factors with and without for loops.

12.2.1 Prime number

Define a function named as prime that checks if an integer is prime. The function must accept the integer as an argument, and return TRUE if the integer is prime, otherwise it must return FALSE.

Call your function with the argument as 197.

12.2.2 Factor

Define a function named as factor that checks if an integer is a factor of another integer. The function must accept both the integers as arguments, and return TRUE if the integer is a factor, otherwise it must return FALSE.

Call your function with the arguments as (19,85)

12.2.3 Prime factors

Define a function named as prime_factors that returns the prime factors of an integer. The function must use the functions prime and factor.

Call the function with the argument as 1234567, and print the returned object, which should be the prime factors of the number.

12.2.4 Prime factors code: Time

Record and print the time taken to execute the function prime_factors for the integer 1234567.

12.2.5 Prime number: Without for loop

Update the function prime so that it works without a for loop. Name the updated function as prime_nofor. Call the function prime_nofor with the argument as 197.

12.2.6 Prime factors: Without for loop

Update the function prime_factors so that it works without a for loop. Name the updated function as prime_factors_nofor. The function must use the functions prime_nofor and factor. Call the function prime_factors_nofor with the argument as 1234567, and print the returned object, which should be the prime factors of the number.

12.2.7 Prime factors: Time taken without for loop

Record and print the time taken to execute the function prime_factors_nofor for the integer 1234567. Is it less than the time taken by prime_factors for the integer 1234567?